Subgroups — C₃₁×D₃₈₇ #37562002

Order 23994.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₂₉	—	3	1	no	maximal
3	C₃×C₃₁×C₄₃	D₃	1	1	yes	characteristic
4	C₃₁×D₄₃	—	9	1	no	Hall
5	C₃₁×C₄₃	D₉	1	1	yes	characteristic, complemented, Hall
6	D₃₈₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₉×C₃₁	—	43	1	no	maximal, Hall
8	C₉×C₄₃	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
9	C₉×C₃₁	D₄₃	1	1	yes	characteristic, complemented, Hall
10	D₁₂₉	—	3	1	no	—
11	D₃×C₃₁	—	129	1	no	—
12	C₃×C₄₃	D₃×C₃₁	1	1	yes	characteristic
13	C₃×C₃₁	D₁₂₉	1	1	yes	characteristic
14	D₄₃	—	9	1	no	Hall
15	C₂×C₃₁	—	387	1	no	Hall
16	C₄₃	D₉×C₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	D₃₈₇	1	1	yes	characteristic, direct product factor, Sylow
18	D₉	—	43	1	no	Hall
19	C₉	C₃₁×D₄₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	129	1	no	—
21	C₃	C₃₁×D₁₂₉	1	1	yes	characteristic
22	C₂	—	387	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	D₃₈₇
commutator, cosocle, hypocenter	C₉×C₄₃	C₂×C₃₁
Frattini	C₃	C₃₁×D₁₂₉
Fitting	C₉×C₃₁×C₄₃	C₂
socle	C₃×C₃₁×C₄₃	D₃
LCS	G ▷ C₉×C₄₃
UCS	C₁ ◁ C₃₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.